Canonically, we don't know. We never got to see a Full Feruchemist (or Mistborn) using all the metals, nor do we have a WoB on this, but theoretically, after seeing era 2 Southern Scadrian tech, many of us suspect that something like that could work.
Just one small thing, I'd change the wording to be clearer that if one fills Nicrosil by leeching Investiture from their other metalminds, they would no longer have any Investiture in those other metalminds, but they could still store, just not tap (because what was stored got converted into Investiture, which then got stored in the Nicrosilmind).